SOLUTION: The expression 2(l+w) may be used to find the perimeter of a rectangle. What are the length and width of a rectangle if the area is 13.5 square units and the length of one side is

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: The expression 2(l+w) may be used to find the perimeter of a rectangle. What are the length and width of a rectangle if the area is 13.5 square units and the length of one side is       Log On


   

Question 214278This question is from textbook Glencoe Mathematics, Algebra I
: The expression 2(l+w) may be used to find the perimeter of a rectangle. What are the length and width of a rectangle if the area is 13.5 square units and the length of one side is 1/5 the measure of the perimeter? This question is from textbook Glencoe Mathematics, Algebra I

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The expression 2(l+w) may be used to find the perimeter of a rectangle.
What are the length and width of a rectangle if the area is 13.5 square units
and the length of one side is 1/5 the measure of the perimeter?
:
Area:
L*W = 13.5
:
"length of one side is 1/5 the measure of the perimeter?"
L = 1%2F5*2(L+W)
L = .4(L+W)
L = .4L + .4W
L - .4L = .4W
.6L = .4W
L = %28.4W%29%2F.6
L = 2%2F3W
then replace L in the area equation
2%2F3W*W = 13.5
2%2F3W^2 = 13.5
Multiply both sides by 3
2W^2 = 40.5
divide both sides by 2
W^2 = 40.5%2F2
W = sqrt%2820.25%29
W = 4.5 is the width
then
L = 2%2F3*4.5
L = 3 is the length
;
;
Check solution, see if it is true in the statement
"length of one side is 1/5 the measure of the perimeter?"
3 = .2*2(3 + 4.5)
3 = .4(7.5)
3 = 3